In the case of wiper blades in accordance with the species, the supporting element is supposed to guarantee the most uniform possible distribution of the wiper blade application force originating from the wiper arm connected to a wiper blade on the windshield over the entire wiper field being covered by the wiper blade. Because of a corresponding curvature of the unstressed supporting element—i.e., when the wiper blade is not adjacent to the windshield—the ends of the wiper strip that is applied completely to the window during wiper blade operation are stressed by the then tensioned supporting element on the windshield, even though the curvature radii of spherically curved vehicle windshields change with every wiper blade position. The curvature of the wiper blade must therefore be somewhat greater than the greatest curvature measured in the wiper field on the to-be-wiped windshield. The supporting element thereby replaces the expensive supporting bracket design with two spring rails arranged loosely in the wiper strip as is the practice with conventional wiper blades.